Control Model for an Elastomer Extrusion Process Obtained via a Comparative Analysis of Data Mining and Artificial Intelligence Techniques

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Polymer-Plastics Technology and Engineering

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Control Model for an Elastomer Extrusion Process Obtained via a Comparative Analysis of Data Mining and Artificial Intelligence Techniques

F. Javier Martínez-de-Pisóna; Alpha V. Perníaa; Julio Blancob; Ana Gonzáleza; Ruben Lostadoa a EDMANS Group (http://www.mineriadatos.com), Departamento de Ingeniería Mecánica, Universidad de La Rioja, Spain b IDG Group (http://www.mineriadatos.com), Department of Mechanical Engineering, Universidad de La Rioja, Spain Online publication date: 07 July 2010

To cite this Article Martínez-de-Pisón, F. Javier , Pernía, Alpha V. , Blanco, Julio , González, Ana and Lostado, Ruben(2010)

'Control Model for an Elastomer Extrusion Process Obtained via a Comparative Analysis of Data Mining and Artificial Intelligence Techniques', Polymer-Plastics Technology and Engineering, 49: 8, 779 — 790 To link to this Article: DOI: 10.1080/03602551003749585 URL: http://dx.doi.org/10.1080/03602551003749585

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Polymer-Plastics Technology and Engineering, 49: 779–790, 2010 Copyright # Taylor & Francis Group, LLC ISSN: 0360-2559 print=1525-6111 online DOI: 10.1080/03602551003749585

Control Model for an Elastomer Extrusion Process Obtained via a Comparative Analysis of Data Mining and Artificial Intelligence Techniques F. Javier Martı´nez-de-Piso´n1, Alpha V. Pernı´a1, Julio Blanco2, Ana Gonza´lez1, and Ruben Lostado1 1

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EDMANS Group (http://www.mineriadatos.com), Departamento de Ingenierı´a Meca´nica, Universidad de La Rioja, Spain 2 IDG Group (http://www.mineriadatos.com), Department of Mechanical Engineering, Universidad de La Rioja, Spain

Some elastomer profile extrusion processes in the automotive industry are still hard to control, generally because they are open loop systems with continual changes in manufacturing conditions. It is at the start-up stage that most time and raw materials are lost. This article describes the development of a dynamic extruder velocity control model that is capable of learning from good start-ups in earlier in manufacturing processes. The process of creating the model focuses on selecting the best technique from a set of data mining (DM) and artificial intelligence (AI) algorithms, which are put to the test with a database containing historical data on the start-up processes that have reached the steady state most quickly in the past. With the new models obtained, the process can be automated, and the time required for start-up in profile manufacturing can be reduced. This will result in increased output, higher quality, less faulty material and lower stress levels among production workers. Keywords Artificial intelligence; extrusion

Data

mining;

Elastomer

INTRODUCTION The automotive industry uses many different long, rubber profiles which are fitted on vehicles as door and window seals to reduce noise and vibration and stop air and water from getting into vehicles. Similar profiles are also used to seal off parts of vehicles, in upholstery, in tyre treads and to protect shock absorbers. Profiles fitted on windows also reduce friction and prevent the glass from wearing when windows are opened and closed. Vehicle manufacturers now require profile suppliers to meet extremely high quality standards. Profiles that fail Address correspondence to F. J. Martı´nez-de-Piso´n, EDMANS Group (http://www.mineriadatos.com), Departamento de Ingenierı´a Meca´nica, Universidad de La Rioja, Spain. E-mail: fjmartin@ unirioja.es

to meet all the requirements in terms of shape, size and finish cannot be fitted properly, and this may have knock-on effects on the whole assembly line. The rubber used must make profiles capable of withstanding frequent impacts and environmental attacks throughout their useful lifetimes. Manufacturers are also required to speed up profile design and manufacturing processes because of the ever faster rate at which new vehicle models are being produced.

The Extrusion Process One of the most important stages of the manufacturing process for these profiles is extrusion. Profiles of this type are extruded as follows: the rubber mix in laminated form is pushed by a ram into a heating chamber, where it is heated to a dense, viscous mass. It is then forced through a die to form a long, continuous product. The cross-section of the profiles is determined by the shape of the opening in the die. When they exit the die, profiles are cooled in air or water, or by contact with a cold surface, and then harden gradually as they lie on a conveyor. The input material for the extrusion process comprises a blend of rubber and other components such as carbon black, plasticising oils, vulcanising agents and other additives to give the end product the specific elasticity, colour and strength required. Extrusion is a complex process and the behaviour of several factors which might prevent profiles of the required size and design from being obtained must be monitored[1,2]. The most important of these factors include uneven flow, distortions in extruded material, profile geometry and certain parameters such as temperature, pressure and ram speed. Complicated profiles may require up to three single-ram extruders (Fig. 1) feeding material simultaneously to a

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FIG. 1. Injector fed by three extruders.

single die[3]. This enables different mixes to be used to suit the characteristics required for each part of the profile. In recent years techniques based on finite elements (FEM), data mining (DM), multivariate statistics and artificial intelligence (AI) have revolutionised the study of extrusion processes for various materials[4–10]. In particular, neural networks have been used in extrusion processes of all types[11–15] because of the ease with which they can model non-linear systems. Applications in elastomers can be found in references[16–19]. Alternatives to neural networks include Support Vector Machines (SVM) and new process modelling techniques[20,21]. Start-Up in Extrusion Processes Many extrusion processes for elastomer profiles for the automotive industry currently continue to be started up manually, because the complexity of the profiles, the differences in their geometries, the variability in the composition of the rubber used and the difficulty of automatically obtaining a variable to indicate the quality of the end product have so far prevented any adequate control system from being set in place. Each time an extrusion process for a particular product needs to be started up, the machine operator manually adjusts the process variables until a steady state for production of a good quality profile is achieved. The main variables adjusted are the ram speeds and the temperatures of the different heating zones. Depending on the skill of the operator and the complexity of the profile to be manufactured, start-up can take a considerable time and entail substantial wastage of raw material. Moreover, production workers may be under a great deal of pressure. To solve this problem, in Martı´nez-de-Piso´n et al.[21] we proposed a method for extracting good start-ups from the

historical database and developed a control model for three extruders based on SVM for determining the required velocity on each one in line with the velocity, temperature and pressure recorded at an earlier time. This paper describes the development of a new, more precise control model, which is more robust to process variations than the previous one. The process of creating the model focuses on selecting the best technique from a set of data mining (DM) and artificial intelligence (AI) algorithms which are which are put to the test with a database containing historical data on the start-up processes that have reached the steady state most quickly in the past. This method enables the abilities of different techniques to develop optimal predictive models to be compared, and enables the technique best suited to each extruder in the process to be reliably selected. With the new models obtained, the process can be automated and the time required for start-up in profile manufacturing can be reduced. This will result in increased output, higher quality, less faulty material and lower stress levels among production workers. We present the process of data acquisition, description and selection of the most significant variables and extraction of the best start-up curves for setting up the database used for training and validating models. Then, we explain how the best models for predicting extruder velocities are obtained from a set of DM and AI techniques, followed by the results and conclusions. CREATING THE TRAINING DATABASE To create a database to train and validate models, good process start-ups must be detected. In Martı´nez-de-Piso´n et al.[20] explains in more detail the method used to extract these data and create the database. Good and bad start-ups can be located clearly by analysing the temperature of the principal extruder. Start-ups are considered as good when that temperature reaches the steady state and remains there for more than 60 minutes. Figure 2 shows how different start-up attempts appear for a problematic profile that required more than 400 minutes before manufacturing could begin. The database contains 27 variables, which include the profile type, date and time when the data were recorded. There are 25 variables which correspond to temperatures and pressures in different areas of the extruders and the velocities of the principal extruder and the two secondary extruders (Table 1). Principal component analysis (PCA) is applied to these last 25 variables and those which have the most effect on the variability of data are selected. Eventually the 9 variables with the most influence on the first two principal axes (PC1 and PC2) were selected. Between them they explain over 70% of the variance in data. They are in fact the real temperature, velocity and pressure in each extruder.

CONTROL MODEL FOR AN ELASTOMER EXTRUSION PROCESS

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FIG. 2. Example of start-up failures observed at principal extrusion temperature.

TABLE 1 Relevant variables and their abbreviations Name EP_C1_T EP_C2_T EP_C3_T EP_CAB_T EP_HUS_T EP_P EP_T EP_V E1_C1_T E1_C2_T E1_C3_T E1_CAB_T E1_HUS_T E1_P E1_T E1_V E2_C1_T E2_C2_T E2_C3_T E2_CAB_T E2_HUS_T E2_P E2_T E2_V HM_V

Description Main Extruder, Body Number 1, Real Temperature Main Extruder, Body Number 2, Real Temperature Main Extruder, Body Number 3, Real Temperature Main Extruder, Head, Real Temperature Main Extruder, Screw, Real Temperature Main Extruder, Real Pressure Main Extruder, Real Temperature Main Extruder, Real Velocity Extruder Number 1 Body Number 1, Real Temperature Extruder Number 1 Body Number 2, Real Temperature Extruder Number 1 Body Number 3, Real Temperature Extruder Number 1 Head, Real Temperature Extruder Number 1 Screw, Real Temperature Extruder Number 1 Real Pressure Extruder Number 1 Real Temperature Extruder Number 1 Real Velocity Extruder Number 2 Body Number 1, Real Temperature Extruder Number 2 Body Number 2, Real Temperature Extruder Number 2 Body Number 3, Real Temperature Extruder Number 2 Head, Real Temperature Extruder Number 2 Screw, Real Temperature Extruder Number 2 Real Pressure Extruder Number 2 Real Temperature Extruder Number 2 Real Velocity Profile velocity

Using the first two principal axes enables us to project the points of operation using the 25 variables for the startups obtained (Fig. 3). Each of these points indicates the position of the process at a given time. Most good start-ups begin in the upper part of the projection and end in the densest area of points when the steady state is achieved. This graph of the points of operation of the start-ups enables each one to be studied. It can also be used to monitor the point of operation of the process in real time. Taking the centre of the highest density area and a threshold distance designated by the analyst, the software developed is capable of determining how many minutes each

FIG. 3. Projection of the operation points of various start-ups using the first two PCA axes.

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start-up requires to reach the stable area corresponding to the steady state for the extrusion process. Using this method, it is possible to select those which reach the steady state most quickly for inclusion in the final training database. A training database is produced for each extruder with 90% of the selected start-ups and a further 10% for testing the models. The data are normalised between zero and one to facilitate convergence of the algorithms and randomly disordered.

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EXTRUDER VELOCITY CONTROL MODEL Design of the Regression Models Figure 4 shows the proposed layout for extruder velocity control. That layout envisages the use of three

FIG. 4. Design of the regression models.

FIG. 5.

models to predict the velocity of each extruder at the following moment (t þ 1) and based on the pressure, temperature and velocity data for the previous moment (t). Pressure variations during the time in question are all so taken into consideration. This makes the model much more robust to sudden changes in pressure due to irregularities in incoming material or to air getting into the system. The control process is applied to the temperatures of the three extruders and the velocities of their rams. Extruder temperature settings are obtained directly from nonlinear regression models drawn up on the basis of real mean temperature curves (Fig. 5) and applied to the PID controllers on the heaters of each extruder. Extruder velocity is determined on the basis of the velocity at the previous moment, the temperature settings obtained from the regression models and the pressures and their derivatives, which are obtained directly from the sensor is on extruders. Temperature differences are not taken into account, because they are high-inertia variables controlled by the PID controllers which are not affected by irregularities in the process. To reduce the number of input variables in the model and eliminate interdependent variables, principal component analysis (PCA) is applied to each group of three similar variables. Tables 2, 3, 4 and 5 show the results of applying PCA to temperature (PCATEMP), velocity (PCAVEL), pressure (PCAPRES) and pressure difference (PCADIFP) variables. In all 4 cases, the first 2 principal axes (PC1 & PC2) explain a high percentage of the accumulated variance (97.3%,

Mean temperature curve, 5% and 95% percentiles of the principal extruder temperature.

CONTROL MODEL FOR AN ELASTOMER EXTRUSION PROCESS

TABLE 2 Results of principal component analysis (PCATEMP) for extruder temperatures

Standard deviation Proportion of variance Cumulative proportion

PC1

PC2

PC3

0.079 0.913 0.913

0.020 0.060 0.973

0.014 0.027 1.000

TABLE 3 Results of principal component analysis (PCAVEL) for extruder velocities

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Standard deviation Proportion of variance Cumulative proportion

PC1

PC2

PC3

0.396 0.938 0.938

0.075 0.033 0.972

0.069 0.029 1.000

Selecting the Best Data Mining Techniques To find models that generate a low prediction error, a battery of algorithms are used:








TABLE 4 Results of principal component analysis (PCAPRES) for extruder pressures

Standard deviation Proportion of variance Cumulative proportion

PC1

PC2

PC3

0.345 0.861 0.861

0.122 0.108 0.968

0.066 0.032 1.000





TABLE 5 Results of principal component analysis (PCADIFP) for extruder pressure increases

Standard deviation Proportion of variance Cumulative proportion

PC1

PC2

PC3

0.390 0.854 0.854

0.141 0.111 0.965

0.079 0.035 1.000










97.2%, 96.8% and 96.5% respectively). In this way for each group of 3 variables, 2 new variables are determined, which are a linear combination of the earlier variables and are independent of each other. This method reduces the number of input variables in the models from 12 to 8 (all independent of one another), which substantially improves the models in terms of tackling problems of size and dependence between variables.

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M5P algorithm (M5P): Implements base routines for generating M5Model[22] trees. A decision list for regression problems is generated using separate-andconquer. In each iteration, it builds a model tree using M5 and makes the ‘‘best’’ leaf into a rule. Quinlan’s M5P can learn such piece-wise linear models. M5P also generates a decision tree that indicates when to use which linear model. Multilayer Perceptron (MLP[23,24]): A classifier and predictor that uses backpropagation to classify instances. All nodes in this network are sigmoid, except when the class is numeric. In the latter case, the output nodes become unthresholded linear units. Training is performed with networks that have between 1 and 30 neurons in the hidden layer. RBF[23] Network (RBFN): Implements a normalized Gaussian radial basis function network. It uses the k-means clustering algorithm to provide the basis functions and learns either a logistic regression (discrete class problems) or a linear regression (numeric class problems). In addition, a symmetric multivariate Gaussian distribution is fitted to the data from each cluster. If the class is nominal, it uses the given number of clusters per class. It standardizes all numeric attributes on a zero mean and unit variance. Linear Regression (LINREG): A class for using linear regression for prediction. Simple Linear Regression (SIMPLR): Uses only the best attribute to obtain the model. It is useful for comparing with other algorithms. LeastMedSq[25] (LMSQ): Implements a least median squared linear regression to make predictions. Least squared regression functions are generated from random sub-samples of the data. The least squared regression that has the lowest median squared error is chosen as the final model. IBk[26] (IBk): A version of the k-nearest neighbour algorithm. K is the number of neighbours to be used. It also permits the use of distance weighting. As it is a lazy algorithm, there is no training time. Support Vector Machines (SVM): Support Vector Machines[27] (SVM) are powerful automatic learning structures based on the statistical theory of learning. Basically, SVMs only use information within the decision borders (called support vectors) and, by means of quadratic programming (QP), they attempt to induce linear or hyperplain separators which maximise the minimum distance between classes. In order to process non-linear ratios, SVMs use kernel functions to project the information in spaces of greater dimensionality and

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then transform them into linearly separable classes. SVM offers an improvement over traditional learning methods because of the size of the network is not established from the outset and the maximum generalisation level is guaranteed mathematically. The purpose of this work is to determine the algorithm or group of algorithms that provide the best prediction or, in other words, the algorithm that yields the lowest Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE) for other different coils not used for model construction. These errors are:

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n 1X RMSE ¼ ðyðkÞ  ^yðkÞÞ2 n k¼1

ð1Þ

and MAE ¼

n 1X jyðkÞ  ^yðkÞj n k¼1

ð2Þ

where y and ^y are, respectively, the measured and predicted outputs and n is the number of points in the database used to validate the models.

TABLE 6 A 10-fold cross-validation errors for principal extruder velocity modelling (ordered according to mean RMSE)

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Algorithm SVM(C ¼ 0.05) SVM(C ¼ 0.1) SVM(C ¼ 0.01) SVM(C ¼ 0.5) MLP(1) SVM(C ¼ 1.0) RBF(7) RBF(10) RBF(5) RBF(4) RBF(3) IBK(1) IBK(2) RBF(15) RBF(2) IBK(3) M5P MLP(2) LINREG SVM(C ¼ 5.0) MLP(40) MLP(3) MLP(5) RBF(20) MLP(7) MLP(10) MLP(20) MLP(4) SVM(C ¼ 10.0) MLP(30) MLP(15) MLP(25) SVM(C ¼ 25.0) LMSQ SVM(C ¼ 50.0) SIMPLR SVM(C ¼ 100.0) SVM(C ¼ 200.0) SVM(C ¼ 500.0) RBF(30)

RMSEMEAN RMSEMAX RMSEMIN RMSESD MAEMEAN MAEMAX MAEMIN MAESD TIME (s) 0.039 0.039 0.040 0.041 0.041 0.043 0.043 0.043 0.043 0.044 0.044 0.045 0.045 0.045 0.045 0.045 0.046 0.047 0.047 0.051 0.053 0.053 0.054 0.054 0.054 0.054 0.055 0.056 0.056 0.057 0.058 0.061 0.063 0.068 0.072 0.073 0.080 0.085 0.088 0.212

0.041 0.042 0.041 0.044 0.049 0.043 0.046 0.047 0.047 0.047 0.046 0.046 0.046 0.054 0.047 0.048 0.052 0.058 0.049 0.056 0.064 0.062 0.067 0.095 0.072 0.067 0.070 0.073 0.062 0.074 0.068 0.088 0.070 0.100 0.082 0.084 0.095 0.102 0.106 1.332

0.036 0.036 0.037 0.037 0.037 0.037 0.039 0.039 0.038 0.040 0.041 0.043 0.042 0.035 0.044 0.043 0.041 0.034 0.046 0.046 0.036 0.035 0.040 0.038 0.041 0.041 0.041 0.034 0.048 0.046 0.048 0.044 0.053 0.036 0.061 0.058 0.065 0.065 0.065 0.049

0.002 0.002 0.002 0.002 0.003 0.002 0.003 0.003 0.003 0.003 0.002 0.001 0.001 0.006 0.001 0.001 0.003 0.007 0.001 0.003 0.008 0.007 0.010 0.016 0.010 0.009 0.007 0.011 0.004 0.008 0.007 0.012 0.006 0.020 0.007 0.008 0.009 0.010 0.012 0.394

10 models were drawn up for each algorithm and configuration.

0.026 0.026 0.027 0.027 0.029 0.026 0.029 0.030 0.030 0.030 0.031 0.032 0.033 0.031 0.032 0.034 0.032 0.032 0.034 0.034 0.033 0.034 0.033 0.035 0.033 0.033 0.033 0.034 0.036 0.033 0.034 0.035 0.039 0.040 0.043 0.044 0.046 0.048 0.050 0.094

0.027 0.027 0.027 0.028 0.033 0.028 0.030 0.032 0.033 0.032 0.033 0.033 0.036 0.036 0.034 0.035 0.036 0.040 0.035 0.035 0.037 0.041 0.040 0.050 0.042 0.038 0.038 0.040 0.038 0.040 0.038 0.046 0.042 0.058 0.046 0.048 0.052 0.055 0.058 0.492

0.025 0.025 0.027 0.026 0.027 0.024 0.028 0.027 0.027 0.027 0.028 0.030 0.031 0.026 0.031 0.033 0.030 0.024 0.033 0.032 0.027 0.028 0.028 0.028 0.028 0.027 0.027 0.026 0.035 0.026 0.028 0.028 0.036 0.025 0.038 0.038 0.039 0.039 0.040 0.035

0.000 0.001 0.000 0.001 0.002 0.001 0.001 0.002 0.002 0.001 0.001 0.001 0.001 0.003 0.001 0.001 0.002 0.004 0.001 0.001 0.004 0.003 0.004 0.006 0.004 0.004 0.003 0.005 0.001 0.004 0.004 0.005 0.002 0.010 0.002 0.003 0.003 0.004 0.005 0.140

117.2 118.5 103.3 106.6 937.7 130.8 65.6 88.2 55.4 51.5 44.2 1.4 1.9 106.3 38.0 2.3 192.2 1629.4 2.2 175.5 27688.4 2313.3 3697.1 122.8 5024.4 7040.8 13755.2 3040.0 276.7 20477.9 10410.8 17126.2 530.0 5504.9 964.6 8.6 1837.1 3527.1 8957.4 158.3

CONTROL MODEL FOR AN ELASTOMER EXTRUSION PROCESS

To this proposal, 10 models of each type of algorithm’s configuration are trained with 80% of the data and the remaining data (20%) are used for validate each model. WEKA[28] suite and R[29] software are used to process the data and to develop the different models. RESULTS The results of the training and cross validation process for data on the manufacturing of a particularly problematic profile are shown in Tables 6, 7 and 8. These tables show the 10-fold cross-validation errors ordered according

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to the mean RMSE for 10 models trained for each type of configuration and algorithm. The values shown are the mean (MEAN), the maximum (MAX), the minimum (MIN) and the standard deviation (SD) of the 10-fold cross-validation errors for RMSE and MAE for each group of 10 models created for each type of configuration and algorithm. Training and validating 10 models for each type reduces errors due to cases where a local minimum is reached, and improves the actual estimation of the level of precision attained by each algorithm with each configuration.

TABLE 7 A 10-fold cross validation errors for extruder 1 velocity modelling (ordered according to mean RMSE)

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Algorithm SVM(C ¼ 5.0) MLP(2) MLP(3) MLP(1) SVM(C ¼ 10.0) LINREG SVM(C ¼ 1.0) MLP(7) MLP(25) MLP(10) MLP(4) MLP(20) MLP(5) SVM(C ¼ 25.0) MLP(15) MLP(30) SVM(C ¼ 0.5) SVM(C ¼ 50.0) MLP(40) SVM(C ¼ 100.0) IBK(2) IBK(3) IBK(1) SVM(C ¼ 200.0) SVM(C ¼ 0.1) M5P SVM(C ¼ 0.05) SVM(C ¼ 500.0) SVM(C ¼ 0.01) RBF(2) RBF(3) RBF(4) RBF(10) RBF(5) RBF(7) SIMPLR RBF(15) RBF(20) LMSQ RBF(30)

RMSEMEAN RMSEMAX RMSEMIN RMSESD MAEMEAN MAEMAX MAEMIN MAESD TIME (s) 0.045 0.048 0.048 0.049 0.049 0.051 0.053 0.053 0.053 0.053 0.054 0.054 0.055 0.056 0.057 0.060 0.060 0.062 0.066 0.067 0.067 0.068 0.070 0.071 0.071 0.071 0.072 0.075 0.075 0.082 0.082 0.082 0.083 0.083 0.083 0.087 0.095 0.097 0.184 0.337

0.050 0.064 0.059 0.063 0.057 0.061 0.057 0.069 0.073 0.067 0.066 0.071 0.068 0.065 0.067 0.071 0.063 0.070 0.098 0.078 0.070 0.071 0.078 0.092 0.073 0.081 0.075 0.094 0.078 0.084 0.084 0.085 0.086 0.085 0.093 0.097 0.150 0.115 0.213 2.070

0.038 0.041 0.031 0.039 0.041 0.043 0.049 0.036 0.036 0.039 0.038 0.041 0.047 0.044 0.041 0.046 0.058 0.049 0.045 0.051 0.064 0.065 0.063 0.052 0.069 0.064 0.070 0.055 0.072 0.077 0.080 0.081 0.079 0.080 0.076 0.084 0.069 0.078 0.152 0.100

0.004 0.008 0.009 0.008 0.005 0.006 0.003 0.012 0.011 0.010 0.010 0.011 0.008 0.007 0.010 0.010 0.002 0.008 0.015 0.009 0.002 0.002 0.004 0.012 0.002 0.005 0.002 0.011 0.002 0.002 0.002 0.002 0.002 0.002 0.005 0.004 0.023 0.013 0.021 0.610

Ten models were drawn up for each algorithm and configuration.

0.031 0.034 0.033 0.038 0.033 0.035 0.035 0.033 0.034 0.033 0.035 0.034 0.036 0.035 0.035 0.038 0.039 0.038 0.042 0.040 0.047 0.048 0.047 0.041 0.045 0.046 0.046 0.043 0.049 0.058 0.058 0.058 0.059 0.059 0.059 0.060 0.064 0.067 0.094 0.158

0.033 0.039 0.042 0.045 0.036 0.040 0.038 0.039 0.042 0.040 0.043 0.042 0.043 0.040 0.040 0.042 0.041 0.042 0.055 0.046 0.049 0.050 0.052 0.051 0.045 0.052 0.046 0.052 0.050 0.061 0.061 0.063 0.064 0.061 0.064 0.065 0.085 0.076 0.110 0.776

0.029 0.028 0.024 0.031 0.030 0.032 0.032 0.026 0.027 0.028 0.028 0.030 0.028 0.030 0.027 0.033 0.037 0.032 0.032 0.033 0.043 0.045 0.042 0.034 0.044 0.043 0.045 0.036 0.049 0.056 0.056 0.057 0.055 0.056 0.053 0.056 0.051 0.057 0.078 0.072

0.002 0.003 0.006 0.005 0.002 0.003 0.002 0.005 0.004 0.004 0.005 0.004 0.005 0.003 0.004 0.004 0.001 0.003 0.007 0.004 0.002 0.001 0.003 0.005 0.000 0.003 0.001 0.005 0.000 0.002 0.002 0.002 0.003 0.001 0.003 0.003 0.010 0.006 0.012 0.218

231.7 1625.5 2294.1 954.9 393.9 26.1 126.7 5035.2 17116.4 7036.0 3020.7 13734.9 3692.7 804.3 10390.5 20482.5 116.3 1519.8 27614.9 3117.7 1.6 2.4 1.6 6281.3 103.4 188.9 105.5 16623.6 157.3 51.0 45.1 51.6 74.9 55.7 79.9 5.8 91.4 109.3 5541.5 144.9

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The value used in the configuration of each algorithm is shown in brackets: in SVM this is the penalty constant C, in MLP it is the number of neutrons in the hidden layer, in IBK it is the number of k-neighbours considered and in RBF it is the number of neurons=clusters used. The last column shows the time required to draw up the 10 models and obtain the cross-validation errors. The calculations were made on a QUAD-CORE OPTERON server running on the Linux SUSE 10.3 OS. The models that required most training time were, of course, the MLP networks with large numbers of neutrons in the

hidden layer (30 & 40) and the SVM with high values of the penalty constant C (200 & 500). From the results obtained it can be observed that the best models were support vector machines (SVM) with low or medium values of C and MLP numeral networks with few neurons in the hidden layer. Principal In the 0.05 and 2.6% for

Extruder case of the principal extruder SVM C values of 0.10 give mean errors of 3.9% for RMSE and MAE: both of which are 0.8% better than the

TABLE 8 A 10-fold cross validation errors for extruder 2 velocity modelling (ordered according to mean RMSE)

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Algorithm SVM(C ¼ 5.0) SVM(C ¼ 10.0) SVM(C ¼ 25.0) SVM(C ¼ 50.0) SVM(C ¼ 100.0) MLP(2) MLP(25) SVM(C ¼ 200.0) MLP(5) MLP(30) MLP(4) SVM(C ¼ 1.0) LINREG SVM(C ¼ 500.0) MLP(7) MLP(15) MLP(20) MLP(1) MLP(10) MLP(40) MLP(3) IBK(2) IBK(3) SVM(C ¼ 0.5) IBK(1) M5P SVM(C ¼ 0.1) SVM(C ¼ 0.05) SVM(C ¼ 0.01) RBF(2) RBF(3) RBF(7) RBF(10) RBF(4) RBF(5) RBF(15) SIMPLR LMSQ RBF(20) RBF(30)

RMSEMEAN RMSEMAX RMSEMIN RMSESD MAEMEAN MAEMAX MAEMIN MAESD TIME (s) 0.030 0.031 0.037 0.041 0.043 0.044 0.045 0.045 0.046 0.046 0.046 0.047 0.047 0.047 0.047 0.047 0.048 0.049 0.050 0.051 0.051 0.053 0.054 0.055 0.056 0.058 0.063 0.064 0.066 0.068 0.069 0.069 0.070 0.071 0.071 0.075 0.077 0.120 0.121 0.318

0.033 0.034 0.045 0.046 0.051 0.056 0.055 0.055 0.061 0.060 0.059 0.052 0.056 0.060 0.063 0.052 0.055 0.055 0.059 0.061 0.057 0.055 0.056 0.058 0.059 0.069 0.069 0.067 0.068 0.070 0.072 0.072 0.077 0.074 0.075 0.096 0.080 0.165 0.270 2.084

0.028 0.028 0.032 0.036 0.039 0.034 0.031 0.039 0.036 0.035 0.041 0.045 0.041 0.039 0.037 0.042 0.038 0.042 0.042 0.039 0.040 0.047 0.051 0.051 0.051 0.044 0.056 0.060 0.065 0.066 0.066 0.067 0.063 0.068 0.068 0.059 0.073 0.054 0.071 0.069

0.001 0.002 0.004 0.003 0.004 0.006 0.007 0.006 0.007 0.010 0.006 0.003 0.005 0.008 0.007 0.003 0.006 0.004 0.006 0.008 0.004 0.003 0.002 0.003 0.003 0.008 0.004 0.002 0.001 0.001 0.002 0.002 0.004 0.002 0.002 0.010 0.003 0.038 0.062 0.622

Ten models were drawn up for each algorithm and configuration.

0.022 0.022 0.025 0.026 0.027 0.031 0.030 0.028 0.030 0.030 0.030 0.032 0.030 0.029 0.031 0.031 0.031 0.034 0.032 0.035 0.034 0.037 0.039 0.038 0.037 0.038 0.045 0.048 0.051 0.054 0.055 0.055 0.053 0.056 0.056 0.054 0.056 0.066 0.070 0.141

0.023 0.023 0.028 0.029 0.031 0.039 0.036 0.034 0.037 0.038 0.037 0.035 0.036 0.036 0.038 0.034 0.036 0.039 0.036 0.041 0.037 0.040 0.041 0.039 0.039 0.042 0.047 0.049 0.052 0.055 0.057 0.057 0.058 0.058 0.058 0.062 0.057 0.097 0.122 0.768

0.021 0.020 0.023 0.024 0.025 0.025 0.023 0.025 0.025 0.025 0.027 0.030 0.028 0.025 0.025 0.028 0.028 0.028 0.029 0.027 0.029 0.034 0.037 0.036 0.036 0.032 0.043 0.046 0.051 0.052 0.053 0.051 0.049 0.054 0.054 0.043 0.053 0.036 0.047 0.045

0.001 0.001 0.002 0.002 0.002 0.004 0.004 0.003 0.003 0.005 0.003 0.002 0.003 0.004 0.004 0.002 0.002 0.004 0.003 0.005 0.002 0.002 0.001 0.001 0.001 0.003 0.002 0.001 0.000 0.001 0.001 0.002 0.003 0.001 0.001 0.006 0.002 0.019 0.024 0.221

265.7 429.2 980.6 1840.8 3701.8 1616.1 17091.9 7256.5 3673.2 20505.2 3006.3 118.1 7.8 18250.9 5018.3 10387.3 13755.1 948.0 7034.9 27564.8 2303.9 1.2 1.3 110.8 1.6 148.8 101.4 103.2 137.2 51.8 44.5 66.4 75.4 51.1 55.3 92.8 2.6 5474.2 109.6 144.3

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FIG. 6. Real and predicted velocity of principal extruder tested with new start-up curves.

average RMSE and MAE with linear models (LINREG). The MLP neural network with a single neuron in the hidden layer give very similar results (RMSEMEAN ¼ 4.1%, MAEMEAN ¼ 2.9%). Next, the neural networks based on radial base functions (RBF) with a few neurons=clusters in the input layer and IBK and M5P models. The results for these models are similar to those for linear regression models (LINREG). Finally, MLP and RBF with large numbers of neurons and SVM with high values of C are the worst performing models. In line with the tables in the RMSEMIN and MAEMIN columns, it can be observed that MLP networks with few neurons (3, 4, 5) can develop models with lower RMSE and MAE cross-validation errors (3.4% and 2.4%, respectively) which are practically the same as some SVM (C between 0.01 and 1.0) or some RBF with 4–15 clusters. This seems to indicate that the most effective control model for the main extruder is likely to be an MLP network with few neurons, an RBF model with a range of between 4 and 15 neurons or an SVM model with a range of C between 0.5 and 1.0.

TABLE 9 Testing errors in the models selected

Device

Type and configuration of best model

Principal Extruder MLP with 2 neurons Extruder One MLP with 3 neurons Extruder Two SVM with C ¼ 10.0

RMSE MAE 3.51% 3.22% 3.02%

2.71% 2.86% 2.14%

Finally, it was decided to seek the best model with an MLP with two neurons in the hidden layer because, as can be seen in Table 6, a model was found with a cross-validation error of 3.4% for RMSE and 2.4% for MAE (RMSEMIN and MAEMIN). Figure 6 shows the behaviour of the model obtained with start-up curves for the principal extruder not included in the training database, and Table 9 shows the testing errors for those same data. Extruder 1 In the case of extruder 1, SVM with C ¼ 5.0 gave mean errors of 4.5% for RMSE and mean values of 3.1% for MAE. In this case the improvement over the results given by linear models (LINREG) is less marked (a difference of 0.6% in RMSE and 0.4% in MAE). MLP neural networks with 1, 2 and 3 neurons give slightly worse models, but the three-neuron network is capable of finding better models (lower RMSEMIN), as it achieves a model with RMSEMIN ¼ 3.1% and MAEMIN ¼ 2.4%, compared to the figures of 4.3% and 3.2% for the linear model (LINREG) and 3.8% and 2.9% for an SVM with C ¼ 5.0. In this case, it was finally decided to use an MLP with three neurons in the hidden layer to seek the best model for the velocity of extruder 1. Figure 7 shows the prediction capabilities of a model developed with new curves not used in the training stage and Table 9 shows the testing errors. Extruder 2 Finally, on extruder 2, SVM with C ¼ 5.0 gives an RMSEMEAN of 3.0% and a MAEMEAN of 2.2%. In this

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FIG. 7. Real and predicted velocity of extruder one tested with new start-up curves.

FIG. 8.

Real and predicted velocity of extruder two tested with new start-up curves.

case the results are substantially better than those obtained with linear models (LINREG) (drops of 1.7% in RMSEMEAN and 0.8% in MAEMEAN). The first five places in the table are occupied by SVM-based models, followed by various MLP with between two and 30 neurons in the hidden layer. Moreover, SVM with C ¼ 10.0 and 5.0 provide the best models (lowest RMSEMIN and MAEMIN). In this case, SVM with C ¼ 10.0 gives a model with an RMSE of 2.8% and a MAE of 2.0%. The algorithm selected is the SVM with C ¼ 10.0. Figure 8 shows the velocity predicted by the model compared with the actual velocity for start-up curves on extruder 2 not used in creating the model. The final testing errors can be seen in Table 9.

CONCLUSIONS This paper proposes a new velocity control model for the extruders used to manufacture rubber profiles for automobiles, developed on the basis of information stored on past good start-ups. The control model can predict the velocity of each extruder precisely, based on setting temperatures, velocities and main pressures at a previous time. Its inputs also include the pressure variations in each extruder, which makes it more robust to changes caused by irregularities in the infeed material or by air getting into the extruders. The process begins with the extraction and modelling of the start-up curves that have resulted in the fastest transition to steady state, using the methods proposed in

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CONTROL MODEL FOR AN ELASTOMER EXTRUSION PROCESS

Martı´nez-de-Piso´n et al.[21]. Next, a training and validation database is generated with 90% of the curves. This database is used to train and validate the models. The remaining 10% of the data are reserved to enable tests to be run with data not used to create the regression models. Once the databases are obtained, the next step is to create various models based on a set of algorithms from data mining (DM) and artificial intelligence (AI). The search method is based on obtaining the 10-fold cross-validation RMSE and MAE errors for each type of algorithm and configuration. To reduce the likelihood of finding local minimums, 10 models of each type and configuration are created and statistical error values are obtained. The techniques selected include linear and non-linear algorithms, so a wide range of adjustment possibilities is covered. With 10-fold cross-validation errors it is possible to determine with a high level of assurance what techniques are unlikely to generate the most precise, most generally applicable models for each extruder in the process. Once the most suitable technique has been determined, regression model for each extruder is created and implemented in the control algorithm. A comparative analysis of linear and nonlinear regression techniques reveals precisely which should be used and what advantage is each technique has over the others. Using these regression models for start-up curves enables the start-up process to be automated based on data from manual start-ups. In other words, a manual process is converted to an automatic process by means of implicit knowledge extracted from the historical database of the extrusion process. As a case study, the models obtained for a profile which gave rise to considerable manufacturing problems are presented. The best models in this case are MLP networks with few neurons in the hidden layer for extruder 1 and the principal extruder, and SVM for extruder 2. Finally, the new control system has proved itself to be more precise in calculating velocities and more robust to disturbances than systems developed in earlier studies. ACKNOWLEDGMENTS The authors thank the ‘‘Direccio´n General de Investigacio´n’’ of the Spanish Ministry of Science and Innovation for the financial support of the projects DPI2006-03060, DPI2006-14784, DPI-2006-02454 and DPI2007-61090; and the European Union for the project RFS-PR-06035. Finally, the authors also thank the Autonomous Government of La Rioja for its support through the 3 Plan Riojano de I þ D þ i. REFERENCES 1. Qingfeng, W.; Nanqiao, Z.; Bing, L.; Ping, Z. Study on the effect of axial vibration of screw in plasticating process (extrusion part). Polym. Plastics Technol. Eng. 2003, 47, 318–324.

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